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$$
	\textlangle E_{f}\textrangle = E_{i} \left(1 - \frac{2\mu}{\left(\mu+1\right)^{2}}\left[1 + \mu sin^{2}\chi + \frac{E_{int}}{E_{i}}\left(\frac{\mu+1}{2\mu}\right) - cos\chi\sqrt{1 - \mu^{2}sin^{2}\chi - \frac{E_{int}}{E_{i}}\left(\mu+1\right)}\right]\right)
$$

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